Not CAA, but CASA accept them as long as there is a regular print out which is filed as a 'true copy' unless the eLog is locked with changes being tracked
I'm not sure what reason you give to the CAA not accepting them. I have maintained solely an electronic log for the last 3 years (in the UK), and a printed copy with the pages signed has sufficed in company audits, and all FCL matters. I used it with the counter service just last monday for the addition of ratings. It is true that you could technically go back and change your flying history and re-print it, but you don't, besides if you had this nature you could add falsified flights into a handwritten log as you go along... perhaps given that this has to be an acceptable means of logging flight moving forward there might be a commercial edge to a company that design a mechanism to add security in this respect?
Approved regular syncing with a cloud based system (to which the relevant authority has access), which can flag up and log changes made retrospectively to the essential flight information required by part-fcl, making them available for assessment by the authority should they chose to make routine checks whilst undergoing company audits etc (not to prevent the changes being made as they may be legitimate, but to draw attention to those flights in particular should someone wish to determine their authenticity). If the system was thought through and approved one would think that it could update your basic flight history, via the cloud, to your personal CAA account directly - no need for handing in paper copies.
Maybe this would be considered a little OTT and perhaps 'Big Borther'y, but there is nothing particularly private in the basic particulars of logged flights, and we need to make them available to the CAA in any case. If a developer were to discuss is with the CAA (LogTen are you listening), and come up with an acceptable, practical solution, they may just wipe the floor with the others.